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Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result
[Estimées de rigidité pour les champs incompatibles comme conséquence du résultat div-rot de Bourgain et Brezis]
Sergio Conti1 ; Adriana Garroni2 
1 Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany
2 University of Rome, Sapienza, P.le A. Moro 2, 00185 Rome, Italy
Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 155-160.

Dans cette note, nous démontrons qu’une estimée de rigidité et une inégalité de Korn pour des champs avec des valeurs matricielles dont l’incompatibilité est une mesure bornée peuvent être obtenues comme conséquence d’une décomposition de Hodge avec intégrabilité critique dû à Bourgain et Brezis.

In this note we show that a sharp rigidity estimate and a sharp Korn’s inequality for matrix-valued fields whose incompatibility is a bounded measure can be obtained as a consequence of a Hodge decomposition with critical integrability due to Bourgain and Brezis.

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DOI : 10.5802/crmath.161
Classification : 49Q20, 74C15, 53C24
Keywords: rigidity estimates, div-curl systems, Korn inequality, plasticity, incompatible fields, Hodge decomposition
Mot clés : estimée de rigidité, systèmes div-rot, inégalité de Korn, plasticité, champs incompatibles, décomposition de Hodge

Sergio Conti 1 ; Adriana Garroni 2

1 Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany
2 University of Rome, Sapienza, P.le A. Moro 2, 00185 Rome, Italy
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Sergio Conti and Adriana Garroni},
     title = {Sharp rigidity estimates for incompatible fields as a consequence of the {Bourgain} {Brezis} div-curl result},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {155--160},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
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     year = {2021},
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     language = {en},
}
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Sergio Conti; Adriana Garroni. Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 155-160. doi : 10.5802/crmath.161. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.161/

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